Lavelli attended the Browns' first training camp in 1946. Competition was fierce for a spot on the roster, but Lavelli was one of the men who made it. He was up against a number of National Football League veterans and former college stars. "The toughest game I ever played in was the first intrasquad scrimmage game," he said later. "Nobody talked to each other for two days." He joined an offense that featured quarterback Otto Graham, fullback Marion Motley, placekicker Lou Groza and fellow end Mac Speedie. Lavelli quickly became Graham's top passing target and led the AAFC in receiving as a rookie with 40 receptions and 843 yards. The Browns made it to the league championship that season, and Lavelli caught the game-winning touchdown in a 14–9 victory over the AAFC's New York Yankees. The victory "didn't mean so much then, but as time goes on, it builds," Lavelli said in 2008.
Over the years, Lavelli developed a reputation for making big plays when they counted most, as he had done with his touchdown reception in the Browns' first championship game in 1946. He was nicknamed "Mr. Clutch" in a Pittsburgh Steelers scouting report, although "Gluefingers" – a name bestowed upon him by Browns announcer Bob Neal – was more widely used. He practiced with Graham tirelessly to refine routes and was not afraid to run over the middle, where he risked a pounding from defenders when the ball came his way. "Dante was the greatest guy at catching a ball in a crowd that I have ever seen," Brown once said. Among other innovations, he and Graham also mastered sideline patterns at a time when few teams used them.